\subsection{Renormalize of mean-field equation}
There are some extra term in the renormalization of mean-field equation in path integral approach (Sec. \ref{sec:pathIntRenorm}).  There is extra term of open-channel in $F_{2}$ ($\frac{v_{\vk}^{2}}{i\omega_{n}-\xi_{2}{}_{\vk}}$ in Eqs. \ref{eq:pathInt2:F20}, \ref{eq:pathInt2:F2kMod}).  This basically means that the open-channel occupies the low-k space and close-channel component in low-k is not as large as it should be in simple two-body $\alpha\phi_{k}$.  This term feeds back to open-channel coupling and shifts the resonance position.  This seems to have no 2-body counterpart and therefore cannot be simply put into a two-body experiment parameter.  And we probably do not need to worry about it in renormalization.  Maybe we can put it into some compact form though.  Nevertheless, we probably still need to express it in a way of compact parameter that is measurable in experiment sense.  

